A382088 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x * B(x)^3) ), where B(x) = 1 + x*B(x)^4 is the g.f. of A002293.

1, 1, 9, 178, 5549, 237456, 12945037, 858203872, 67035559257, 6029839290880, 613862192499281, 69777500840918784, 8760124051527691141, 1203852634738613966848, 179746834136205848167125, 28975042890917781500747776, 5015346425440407318539964593, 927775677566572703009955053568

Offset: 0

Author

Seiichi Manyama, Mar 15 2025

Keywords

• nonn

Crossrefs

Cf. A382086, A382087, A382089.

Cf. A002293, A377833, A382038.

Programs

PARI

a(n) = if(n==0, 1, (n-1)!*sum(k=0, n-1, (n+1)^(n-k-1)*binomial(3*n+k-1, k)/(n-k-1)!));

Formula

E.g.f. A(x) satisfies A(x) = exp(x*A(x) * B(x*A(x))^3).

a(n) = (n-1)! * Sum_{k=0..n-1} (n+1)^(n-k-1) * binomial(3*n+k-1,k)/(n-k-1)! for n > 0.

E.g.f.: exp( Series_Reversion( x * (1-x)^3 * exp(-x) ) ).